CNN's president on Wednesday denounced the White House for its "total and complete lack of understanding" of the consequences of attacks against the media after the cable news network's New York office and several prominent Democrats were sent pipe bombs.

Feelings were raw over a perceived reluctance by the administration to mention that CNN was sent one of the crude devices, which also went to Hillary Clinton, former President Barack Obama and others.

A fundraising email attacking CNN sent out as the story unfolded deepened that perception. Trump's campaign later apologised for the email.

"The president, and especially the White House press secretary, should understand their words matter," said Jeff Zucker, president of CNN Worldwide.

"Thus far, they have shown no comprehension of that."

CNN has been a frequent target of Trump's "fake news" barbs, and a "CNN sucks" chant broke out at a Monday campaign rally.

Amid that backdrop, some at CNN were angered by an initial tweet by White House press secretary Sarah Sanders that condemned "the attempted violent attacks recently made against President Obama, President Clinton, Secretary Clinton and other public officials," but omitted any reference to CNN.

An hour later she sent another tweet that said the White House's condemnation "certainly includes threats made to CNN as well as current and former public servants".

The president, who has labeled reporters "enemy of the people," condemned the threat of political violence at a campaign rally in Wisconsin on Wednesday evening, and called on the media to end its "hostility".

"The media also has a responsibly to set a civil tone and to stop the endless hostility and constant negative and oftentimes false attacks and stories," Trump said.

The CNN attack was in one respect a case of mistaken identity.

The package that included the explosive device and an envelope containing white powder was addressed to former CIA director John Brennan, a frequent Trump critic.

Brennan is actually a contracted analyst at NBC News, but the package was sent to the Time Warner Center in New York, where CNN's offices are.

CNN's Jim Sciutto and Poppy Harlow were on the air shortly after 10 am, conducting a live interview about the devices sent to politicians when the whooping sound of an alarm went off.

"Excuse me, that sounds like a fire alarm here. We'll keep you posted on that," Sciutto said.

He continued the interview, but after one more question cut to a commercial.

After the break, he and Harlow were gone.

They had evacuated, and correspondent Rene Marsh was hurriedly put on air from a Washington studio.

Wolf Blitzer, who was pulling in to a parking garage in Washington as this was happening, soon joined her.

Sciutto and Harlow then reported by phone from the street, then through a video stream, and then through a full CNN crew.

CNN employees milled about in the streets, along with shoppers in the Time Warner Center mall, which was also evacuated.

Zucker was not among the evacuees.

He was at the network's Atlanta headquarters on Wednesday, where he helped direct coverage from a control room.

Trump did not mention CNN or any of the officials targeted by the device during an afternoon appearance at the White House.

"No one is mentioning the name (CNN)," said network analyst Gloria Borger after Trump's appearance.

"It's as if it can't roll off the tongue unless you're complaining about it."

Less than two hours after the CNN offices were evacuated, Trump's campaign sent a fundraising email to some supporters that specifically targeted CNN and urged recipients to fight back against the "fake news attacks and bias against hardworking Americans".

Campaign chairman Brad Parscale later apologized, saying it was a pre-programmed message that was not caught before news of the pipe bomb came out. Parscale said the campaign does not condone violence against CNN or anyone else.

CNN anchor Chris Cuomo, reporting from the street outside the Time Warner Center as employees began filing back in on Wednesday afternoon, mentioned the many messages of support he had received online and in person.

"You should take good where you find it," Cuomo said, "and you see a country that seems to be universally appalled by what has happened".